Question 5.4: Define the workcells for the given product-machine relationa...
Define the workcells for the given product-machine relational matrix below.
| Products | |||||||||
|
Machines |
M_{ij} | 1 | 3 | 4 | 7 | 2 | 5 | 6 | 8 |
| A | 1 | 1 | 1 | ||||||
| E | 1 | 1 | |||||||
| C | 1 | 1 | 1 | 1 | |||||
| F | 1 | 1 | |||||||
| D | 1 | 1 | 1 | 1 | |||||
| B | 1 | 1 | 1 | ||||||
Step 1: for column i (i = 1, 2,…, n), the binary weight 2^{n-i} is assigned as (2^{7}, 2^{6}, . . . 2^{1}, 2^{0}, respectively. The decimal weight of Row A becomes 2^{7}(1) + 2^{6}(1) + 2^{5}(0) + 2^{4}(0) + 2^{3}(1) + 2^{2}(0) + 2^{1}(0) + 2^{0}(0) = 200, and those for other rows are calculated as below:
|
Machine |
Part | |||||||||
| M_{ij} | 1 | 3 | 4 | 7 | 2 | 5 | 6 | 8 | \sum\limits_{j=1}^{j=8}{2^{n-j}M_{i,j} } | |
| A | 1 | 1 | 1 | 200 | ||||||
| E | 1 | 1 | 17 | |||||||
| C | 1 | 1 | 1 | 1 | 102 | |||||
| F | 1 | 1 | 17 | |||||||
| D | 1 | 1 | 1 | 1 | 54 | |||||
| B | 1 | 1 | 1 | 200 | ||||||
| 2^{(n-j)} | 2^{7} | 2^{6} | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} | ||
Step 2: sort the rows in the order of decreasing decimal weight values as A, B, C, D, E, and F.
|
Machine |
Part | |||||||||
| M_{ij} | 1 | 3 | 4 | 7 | 2 | 5 | 6 | 8 | \sum\limits_{j=1}^{j=8}{2^{n-j}M_{i,j} } | |
| A | 1 | 1 | 1 | 200 | ||||||
| B | 1 | 1 | 1 | 200 | ||||||
| C | 1 | 1 | 1 | 1 | 102 | |||||
| D | 1 | 1 | 1 | 1 | 54 | |||||
| E | 1 | 1 | 17 | |||||||
| F | 1 | 1 | 17 | |||||||
| 2^{(n-j)} | 2^{7} | 2^{6} | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} | ||
Step 3: Repeat step 1 for row j (j = 1, 2,…, m), the binary weight 2^{m-i} is assigned as ( 2^{5}, 2^{4}, . . . 2^{1}, 2^{0}, respectively. The decimal weight of Column 1 becomes 2^{5}(1) + 2^{4}(1) + 2^{3}(0) + 2^{2}(0) + 2^{1}(0) + 2^{0}(0) = 48, and those for other columns are calculated as below:
|
Machine |
Products | |||||||||
| M_{ij} | 1 | 3 | 4 | 7 | 2 | 5 | 6 | 8 | 2^{(m-j)} | |
| A | 1 | 1 | 1 | 2^{5} | ||||||
| B | 1 | 1 | 1 | 2^{4} | ||||||
| C | 1 | 1 | 1 | 1 | 2^{3} | |||||
| D | 1 | 1 | 1 | 1 | 2^{2} | |||||
| E | 1 | 1 | 2^{1} | |||||||
| F | 1 | 1 | 2^{0} | |||||||
| \sum\limits_{i=1}^{i=6}{2^{m-i}M_{i,j} } | 48 | 56 | 12 | 7 | 48 | 12 | 12 | 3 | ||
The columns are then reordered in decreasing values from left to right as 3, 1, 2, 4, 5, 6, 7, and 8.
Step 4: Repeat steps 1, 2, and 3 to get the final result (no more switch when the steps are repeated) as figure below .
Finally, three workcells should be defined, the first one consists of machines A, B, and C, for products 1, 2, and 3; the second one consists of machine C and D for products 4, 5, and 6, and the third one consists of D, E, and F for products 7 and 8.
Note that ROC may not be able to generate workcells for some product-machine relational matrices; since it is not uncommon that the iterative process in ROC leads to an oscillation. This should be solved by introducing more machines of same types. Another scenario is that the finished clusters have an outlier or void; an outlier should be addressed by a machine replication, while no action is needed for a void; the product just skips any operation on the corresponding machine.
